Finer-grained Locking in Concurrent Dynamic Planar Convex Hulls

Of a Semi - Dynamic Convex Hull Algorithm

We obtain new results for manipulating and searching semi-dynamic planar convex hulls (subject to deletions only), and apply them to derive improved bounds for two problems in geometry and scheduling. The new convex hull results are logarithmic time bounds for set splitting and for finding a tangent when the two convex hulls are not linearly separated. Using these results, we solve the followin...

Adaptive Planar Convex Hull Algorithm for a Set of Convex Hulls

The Number of Combinatorially Different Convex Hulls of Points in Lines ∗

Given a sequenceR of planar lines in general position, we can obtain a point set by picking exactly one point from each line in R. We provide exponential upper and lower bounds on the number of combinatorially different convex hulls for point sets that are generated in this manner.

Convex Hulls of Multidimensional Random Walks

Let Sk be a random walk in R such that its distribution of increments does not assign mass to hyperplanes. We study the probability pn that the convex hull conv(S1, . . . , Sn) of the first n steps of the walk does not include the origin. By providing an explicit formula, we show that for planar symmetrically distributed random walks, pn does not depend on the distribution of increments. This e...

Plane and Boundray Extraction from Lidar Data Using Clustering and Convex Hull Projection

In this paper, we propose a new approach to extract planar patches and boundary from a set of LiDAR point cloud. In the beginning, the 3D point cloud set is partitioned and assigned to fixed-size cubes. Secondly, local planar patches are generated by extracting surface normal vectors within each cube. Finally, the global planes are formed by grouping the planar patches. The boundary of global p...